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  • Letter
  • Open Access

Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap

Constantine Yannouleas* and Uzi Landman†

  • School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA

  • *Constantine.Yannouleas@physics.gatech.edu
  • †Uzi.Landman@physics.gatech.edu
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Phys. Rev. Research 3, L032028 – Published 30 July, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032028

Abstract

Exact two-dimensional analytic wave functions for an arbitrary number N of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of exact Hamiltonian numerical diagonalization data. Closed-form analytic expressions are presented for two families of zero-interaction-energy states at given total angular momentum and total spin 0≤S≤N/2 in the neighborhood of the ν=1 filling, covering the range from the maximum density droplet to the first quasihole. Our theoretical predictions for higher-order spatial and momentum correlations reveal intrinsic polygonal, multi-ring crystalline-type structures, which can be tested with ultracold-atom experiments in rapidly rotating traps, simulating quantum Hall physics (including quantum LLL skyrmions).

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Phys. Rev. Research 3, L032028– Published 30 July, 2021
  • Received 12 January 2021
  • Accepted 29 June 2021
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